ETD Collection

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    Spectra of the excited giant gravitons from the two loop dilatation operator
    (2016-09-19) Ali, Abdelhamid Mohamed Adam
    The AdS/CFT correspondence is a conjectured exact duality between type IIB string theory on the AdS5 S5 background and N = 4 Super Yang-Mills theory, a conformal eld theory (CFT), on the boundary of the AdS space. A speci c observable of the CFT, which can be read from the two point correlation function, is the anomalous dimension. In this dissertation we will compute spectra of anomalous dimensions of excited giant gravitons up to two loops in a speci c limit. We are interested in the anomalous dimensions because the AdS/CFT correspondence associates them with energies of states in quantum gravity. We study operators constructed using n Z elds and m Y elds with n << m: In this case m n is a small parameter. At the leading order in m n and at large N, the problem of determining the anomalous dimensions can be mapped into the dynamics of m non-interacting magnons. The subleading terms at two loops, computed for the rst time in this dissertation, induce interactions between the magnons. Even after including this new correction, we nd the BPS operators remain BPS.
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    A collective field theory approach to the large N spectrum of two matrices
    (2008-03-07T12:27:47Z) Cook, Martin
    Abstract The collective field theory technique provides a method of tackling problems with two N × N matrices in the large N limit. The collective field background from one matrix is first found, then the second matrix is introduced into this background as an impurity. Within the context of the AdS/CFT correspondence, this technique can be used to describe gauge theory states in the BMN limit. This dissertation starts by developing the collective field theory technique, firstly in general variables, then for one matrix, and subsequently for two matrices. It goes on to introduce a Yang-Mills interaction term, where two variable identifications are considered. The first is the more traditional angular momentum eigenstate model. The second is a model that directly uses two of the Higgs scalars. This model has been mentioned in the literature, but has not been considered in great depth. The exact two impurity spectrum is found, and the multi-impurity spectrum is found to first order. The resulting energy values match a spectrum that has been found for giant magnons.